Angles formed by Parallel Lines

Transcription

1 Worksheet Answers 1. a = 60, b = 120, c = a = 90, b = 90, c = a = 77, b = 52, c = 77, d = a = 60, b = 120, c = 120, d= 115, e = 65, f =115, g = 125, h =55, I = a = 90, b = 163, c = 17, d = 110, e = They should add up to 180 degrees.

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5 Objectives: Angles formed by Parallel Lines Given one angle measure, find ALL angles formed by 2 parallel lines Identify special angle pairs Use special angle pair rules to find angle measures

6 TRANSVERSAL: A line that intersects two coplanar lines.

7 Corresponding Angles Two angles that are in the same position but on different lines are called corresponding. 1 2

8 New terminology Which angles would you say are interior angles? Which angles would you say are exterior angles?

9 New terminology Interior: between the lines Exterior: outside the lines Alternate: opposite sides of the transversal Same-side: same side of the transversal Give me an example of: A pair of alternate interior angles A pair of same-side interior angles A pair of alternate exterior angles

10 IN YOUR NOTES! Alternate Interior: 4 and 5, 3 and 6 Same-side Interior: 3 and 5, 4 and 6 Alternate Exterior: 1 and 8, 2 and 7 Corresponding: 1 and 5, 2 and 6, 3 and 7, 4 and

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12 Corresponding Angles If the lines are parallel, corresponding angles will be congruent!!!

13 DISCUSS WITH YOUR GROUP: If lines m and n are parallel, which angles are congruent to each other? Discuss in groups: Which angles do you think are congruent? Why do you think they are congruent? Does your group all agree or not? WHAT IS THIS SYMBOL???? l m n

14 Same Side Interior Angles Postulate: If two parallel lines are cut by a transversal, then the pairs of same-side interior angles are supplementary Corresponding Angles Theorem If two parallel lines are cut by a transversal, then the pairs of corresponding angles have the same measure

15 Alternate Interior Angles Theorem: If two parallel lines are cut by a transversal, then the pairs of alternate interior angles have the same measure Alternate Exterior Angles Theorem: If two parallel lines are cut by a transversal, then the pairs of alternate exterior angles have the same measure

16 IN YOUR BINDER IF THE LINES ARE PARALLEL: Alternate Interior: congruent Alternate Exterior: congruent Same-side Interior: supplementary

17 Whiteboard Practice You can always refer back to these slides on my website

18 One angle measure is given. Find the measures of ALL other angles o

19 One angle measure is given. Find the measures of ALL other angles o

20 Which type of angle? 1 2

21 Which type of angle? 1 2

22 Which type of angle? 2 1

23 Which type of angle? 1 2

24 Which type of angle? 1 2

25 Which type of angle? 1 2

26 Which type of angle? 1 2

27 Which type of angle? 1 2

28 Which type of angle? 1 2

29 Which type of angle? 1 2

30 Which type of angle? Corresponding 1 2

31 Which type of angle? Same-side interior 1 2

32 Which type of angle? Corresponding 1 2 WHY ARE THERE TWO ARROWS???

33 What is ALWAYS true about alternate interior angles when two parallel lines are cut by a transversal? They are congruent

34 What is ALWAYS true about same-side interior angles when two parallel lines are cut by a transversal? They are supplementary

35 What is ALWAYS true about alternate exterior angles when two parallel lines are cut by a transversal? They are congruent

36 If the measure of angle 1 is 30 degrees, what is the measure of angle 2? HOW DO YOU KNOW? 1 m 2 = 30 o ; they are alternate exterior 2

37 If the measure of angle 1 is 45 degrees, what is the measure of angle 2? HOW DO YOU KNOW? 1 2 m 2 = 135 o ; they are same-side interior

38 If the measure of angle 1 is 25 degrees, what is the measure of angle 2? HOW DO YOU KNOW? 1 2 m 2 = 25 o ; they are vertical

39 If the measure of angle 1 is 115 degrees, what is the measure of angle 2? HOW DO YOU KNOW? m 2 = 115 o ; they are corresponding 1 2

40 If the measure of angle 1 is 47 degrees, what is the measure of angle 2? HOW DO YOU KNOW? m 2 = 47 o ; they are alternate interior 1 2

41 If the measure of angle 1 is 41 degrees, what is the measure of angle 2? HOW DO YOU KNOW? 1 2 m 2 = 139 o ; they are supplementary

42 If the measure of angle 1 is 41 degrees, what is the measure of angle 2? HOW DO YOU KNOW? 1 2 TRICK QUESTION: These lines aren t parallel. We don t know!

43 If the measure of angle 1 is 40 degrees, what is the measure of angle 2? HOW DO YOU KNOW? m 2 = 140 o ; angle 3 is 40 degrees because it corresponds to angle 1; angle 2 is supplementary with angle 3

44 With algebra Find the value of x. Alt. Ext: congruent 2x + 50 = 4x 10 x = 30 (4x 10) o (2x +50) o

45 With algebra Find the measure of both angles. Same-side interior: supplementary (5x) + (x + 30) = 180 6x +30 = 180 x = o, 125 o

46 Exit Ticket Don t forget your name Hold it up when done ) If m 1 = 84 o, find the measure of ALL other angles. 2) If m 3 = 112 o, find the measure of angle 6. 3) If m 5 = 80 o, find the measure of angle 3. 4) Angle 4 and angle 8 are angles. 5) Angle 2 and angle 7 are angles.

47 Homework Worksheet